NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 21:42 It is currently 24 Apr 2024, 21:42
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

There are n different size pairs of shoes in the box. One

User avatar
lexis
Manager
Manager
Joined: 07 Jan 2008
Posts: 218
Own Kudos [?]: 1927 [1]
Given Kudos: 0
Send PM
There are n different size pairs of shoes in the box. One [#permalink] New post   Updated on: 06 May 2008, 23:20
1
Kudos
There are n different size pairs of shoes in the box. One day, Tan took 2k (2k<2n) shoes out of box to clean. What is the probability that only 1 pair of shoes with the same size was taken out?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!

Originally posted by lexis on 02 May 2008, 10:04.
Last edited by lexis on 06 May 2008, 23:20, edited 1 time in total.
User avatar
lexis
Manager
Manager
Joined: 07 Jan 2008
Posts: 218
Own Kudos [?]: 1927 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   05 May 2008, 22:46
Well, no one left comments here :(
User avatar
farend
Manager
Manager
Joined: 27 Jul 2007
Posts: 55
Own Kudos [?]: 31 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   06 May 2008, 06:47
lexis wrote:
There are n different size pairs of shoes in the box. One day, Tan took 2k (2k<n) shoes out of box to clean. What is the probability that only 1 pair of shoes with the same size was taken out?


I get nC1 * 2n-2C2k-2 / 2nC2k
= (2*k^2-k)/(2*n-1) .
User avatar
farend
Manager
Manager
Joined: 27 Jul 2007
Posts: 55
Own Kudos [?]: 31 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   07 May 2008, 06:42
lexis; Wats the OA ?
User avatar
lexis
Manager
Manager
Joined: 07 Jan 2008
Posts: 218
Own Kudos [?]: 1927 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   07 May 2008, 22:45
farend wrote:
lexis wrote:
There are n different size pairs of shoes in the box. One day, Tan took 2k (2k<n) shoes out of box to clean. What is the probability that only 1 pair of shoes with the same size was taken out?


I get nC1 * 2n-2C2k-2 / 2nC2k
= (2*k^2-k)/(2*n-1) .


u mean nC1=C(n,1)?

U should explain how did U get it. As I see, your answer is not correct.
User avatar
JohnLewis1980
Senior Manager
Senior Manager
Joined: 21 Apr 2008
Posts: 286
Own Kudos [?]: 102 [0]
Given Kudos: 13
Concentration: Industrial Sector
Schools:Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
 Q47  V28
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   08 May 2008, 05:49
My contribution:

Prob=2k/(2n-1)

Reasoning:

What is the prob of taking the appropriate shoe out once you have taken one out before?

1/(2n-1)

Because you have taken 2k shoes out, thus, 2k/(2n-1)

Regards
User avatar
RyanDe680
Manager
Manager
Joined: 27 Jun 2007
Posts: 103
Own Kudos [?]: 338 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   08 May 2008, 09:58
all too often, I see a problem like this and just draw a blank.
User avatar
lexis
Manager
Manager
Joined: 07 Jan 2008
Posts: 218
Own Kudos [?]: 1927 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   08 May 2008, 12:28
JohnLewis1980 wrote:
My contribution:

Prob=2k/(2n-1)

Reasoning:

What is the prob of taking the appropriate shoe out once you have taken one out before?

1/(2n-1)

Because you have taken 2k shoes out, thus, 2k/(2n-1)

Regards


WELL, your answer is not correct.
-----------

Let me explain more about this statement:
For example, there are 5 pairs of shoes A,B,C,D,E
probability to take only one pair of shoes is correct and 1 incorrect pair of shoes (mean 2 different shoes)?

Mean:
Let A1, A2 is correct pair (pretend)
C1,D2 is incorrect pair or C2, E2 or... (pretend)

Hope it helps you solve the general puzzle.

@ RyanDe680: Your avatar is so interesting.
User avatar
lexis
Manager
Manager
Joined: 07 Jan 2008
Posts: 218
Own Kudos [?]: 1927 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   16 May 2008, 03:19
If no one can take the correct answer, I will leave the OA in next week.
User avatar
JohnLewis1980
Senior Manager
Senior Manager
Joined: 21 Apr 2008
Posts: 286
Own Kudos [?]: 102 [0]
Given Kudos: 13
Concentration: Industrial Sector
Schools:Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
 Q47  V28
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   16 May 2008, 07:14
lexis wrote:
JohnLewis1980 wrote:
My contribution:

Prob=2k/(2n-1)

Reasoning:

What is the prob of taking the appropriate shoe out once you have taken one out before?

1/(2n-1)

Because you have taken 2k shoes out, thus, 2k/(2n-1)

Regards


WELL, your answer is not correct.
-----------

Let me explain more about this statement:
For example, there are 5 pairs of shoes A,B,C,D,E
probability to take only one pair of shoes is correct and 1 incorrect pair of shoes (mean 2 different shoes)?

Mean:
Let A1, A2 is correct pair (pretend)
C1,D2 is incorrect pair or C2, E2 or... (pretend)

Hope it helps you solve the general puzzle.

@ RyanDe680: Your avatar is so interesting.


I'm afraid so :oops:

but why? :?:

Don't we agree in the probability to take one complete pair of shoes? i.e. to take the right shoe once you've already take one out?

For me: 1/(2n-1)

Explanation: you take one shoe out, therefore, just 2n-1 shoes remain in the box. The probability to take the right one off is 1/(2n-1), doesn't it?

:| I need to improve my statistic skill.

Thanks for the explanation
avatar
alex1234
Intern
Intern
Joined: 17 May 2008
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   17 May 2008, 00:48
You should try WinGMAT. It is a really good and comprehensive website for preparing yourself for a GMAT exam. Do try it and see for yourself. Try a 24 hour free trial which you get when you sign up.
User avatar
alexsmith
Intern
Intern
Joined: 10 May 2008
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   18 May 2008, 01:52
I agree with alex1234 that wingmat is very helpful for preparing yourself for the math section of GMAT. I love the practice tests and the way they explain each sum with a video. I found it very useful. It is worth trying.
User avatar
cumic
Intern
Intern
Joined: 14 May 2008
Posts: 23
Own Kudos [?]: 113 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   18 May 2008, 10:24
JohnLewis1980 wrote:
My contribution:

Prob=2k/(2n-1)

Reasoning:

What is the prob of taking the appropriate shoe out once you have taken one out before?

1/(2n-1)

Because you have taken 2k shoes out, thus, 2k/(2n-1)

Regards

===============================================

Shoudn't this be solved like this ->

Probability of taking out 2k shoes from total of 2n shoes = 2k/2n
Probability of taking out second compatible shoe = 1/(2n-1)

Hence probability of both events happening together - 2k/2n(2n-1)

Can someone confirm the OA please?

Regards,
Cumic
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10035 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   18 May 2008, 11:29
Expert Reply
Interesting problem. +1

My attempt: \(P=\frac{C^n_k*C^{k}_{1}*(C^2_1)^{k-1}*C^{n-k}_{k-1}}{C^{2n}_{2k}}\)

when 2k>n+1 P=0
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10035 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   18 May 2008, 11:34
Expert Reply
alex1234 wrote:
You should try WinGMAT. It is a really good and comprehensive website for preparing yourself for a GMAT exam. Do try it and see for yourself. Try a 24 hour free trial which you get when you sign up.

alexsmith wrote:
I agree with alex1234 that wingmat is very helpful for preparing yourself for the math section of GMAT. I love the practice tests and the way they explain each sum with a video. I found it very useful. It is worth trying.


alex, please, doesn't think that all here are fools. Be frank and post advertisement in appropriate threads.
User avatar
alexsmith
Intern
Intern
Joined: 10 May 2008
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   28 May 2008, 08:46
I'm just giving my views, I'm not advertising.
Is it so that if someone gives their views about a site which I used for my preparation of GMAT is called advertisement??
I benefited from this site and I want everyone else to also.
I'll keep giving my views about the source what I used for my GMAT entrance and will ask all to just try it once.
I'm sure you will get the results that you are dreaming for.
Thats all I want to say.
User avatar
B
JingChan
Manager
Manager
Joined: 07 Sep 2007
Posts: 66
Own Kudos [?]: 46 [0]
Given Kudos: 0
 Q50  V48
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   29 May 2008, 06:11
Let C(i, k) = iCk = i!/(k!(k-i)!)

Total number of ways to grab shoes:
C(2n, 2k)

Total number of ways to grab only 1 pair:
C(n, 1) * C(n-1, 2k-2) * 2^(k-2)

Answer:
C(n, 1) * C(n-1, 2k-2) * 2^(2k-2) / C(2n, 2k)
(unless 2k > n+1, then prob = 0)

This isn't an official question, right? The variables are awkwardly defined.

Either way, can I get the A, B, C, D, E answers/distractors, I would like to give this problem to a friend.
User avatar
alexsmith
Intern
Intern
Joined: 10 May 2008
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   30 May 2008, 07:42
Hey friends try WinGMAT its really a good site for all people who have problem in GMAT Math and Verbal..
User avatar
lexis
Manager
Manager
Joined: 07 Jan 2008
Posts: 218
Own Kudos [?]: 1927 [0]
Given Kudos: 0
Send PM
Re: There are n different size pairs of shoes in the box. One [#permalink] New post   12 Jun 2008, 04:44
JingChan wrote:
Let C(i, k) = iCk = i!/(k!(k-i)!)

Total number of ways to grab shoes:
C(2n, 2k)

Total number of ways to grab only 1 pair:
C(n, 1) * C(n-1, 2k-2) * 2^(k-2)

Answer:
C(n, 1) * C(n-1, 2k-2) * 2^(2k-2) / C(2n, 2k)
(unless 2k > n+1, then prob = 0)

This isn't an official question, right? The variables are awkwardly defined.

Either way, can I get the A, B, C, D, E answers/distractors, I would like to give this problem to a friend.


Congratulation! You're correct. Your math skill is very good!
The tricky is to require ONLY ONE pair of shoes be same size.
To solve it, we separate two sequences:
1st: There is NO pair of shoes
2nd: There is ONLY ONE pair of shoes be same size
==> Combine: ONLY ONE pair of shoes be same size + NO pair of shoes in rest shoes (2n-2)



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: There are n different size pairs of shoes in the box. One [#permalink]
12 Jun 2008, 04:44
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions